I think people have said that you can take all of your purchases to the hotel gift shop, and they will ship it for you. I haven't tried it myself, but at least this post will bump you up so that someone else might answer.
If you want to ship it home yourself, you'll need to take a box and shipping tape. Probably not convenient if you're flying.
If you happen to be staying at a Disney hotel with a convention center attached, you can take your stuff into the convention center business office, and they will ship it home for you. I have done that.